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LHC Physics Potential Vs. Energy: Considerations for the 2011 Run Chris Quigg*

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LHC Physics Potential Vs. Energy: Considerations for the 2011 Run Chris Quigg* FERMILAB{FN{0913{T Rev. February 1, 2011 LHC Physics Potential vs. Energy: Considerations for the 2011 Run Chris Quigg* Theoretical Physics Department Fermi National Accelerator Laboratory Batavia, Illinois 60510 USA and CERN, Department of Physics, Theory Unit CH1211 Geneva 23, Switzerland Parton luminosities are convenient for estimating how the physics potential of Large Hadron Collider experiments depends on the energy of the proton beams. I quan- tify the advantage of increasing the beam energy from 3:5 TeV to 4 TeV. I present parton luminosities, ratios of parton luminosities, and contours of fixed parton lumi- nosity for gg, ud¯, qq, and gq interactions over the energy range relevant to the Large Hadron Collider, along with arXiv:1101.3201v2 [hep-ph] 1 Feb 2011 example analyses for specific processes. This note ex- tends the analysis presented in Ref. [1]. Full-size figures are available as pdf files at lutece.fnal.gov/PartonLum11/. *E-mail:[email protected] 2 Chris Quigg 1 Preliminaries The 2009-2010 run of the Large Hadron Collider at CERN is complete, with the delivery of some 45 pb−1 of proton-proton collisions at 3:5 TeV per beam to the ATLAS and CMS experiments. The primary objective of the run, to commission and ensure stable operation of the accelerator complex and the experiments, has been achieved, and much has been learned about machine operation. The experiments succeeded in \rediscovering" the standard model of particle physics, and using familiar physics objects such as W ±, Z0, J= , Υ, jets, b-hadrons, and top-quark pairs to tune detector performance. In a few cases, LHC experiments have begun to explore virgin territory and surpass the discovery reach of the Tevatron experiments CDF and D0 [2]. Coming soon is an extended physics run during 2011-2012, with the goal of logging 1 fb−1 by the end of 2011 and perhaps 5 fb−1 by the end of 2012. Still to be decided is whether to raise the proton energy from 3:5 TeV to 4 TeV per beam. The object of this notep is to quantify the enhancedp sensitivity that would follow from running at s = 8 TeV rather than s = 7 TeV by considering some key parton luminosities. The choice of energy impacts the comparison of sensitivities at the LHC and the Tevatron. Taking the long view, it is also important to keep inp mind how much is to be gained by approaching the LHC design energy of s = 14 TeV. Detailed simulations of signals and backgrounds are of unquestioned value for in-depth consideration of the physics possibilities, especially in view of experience gained during the 2009-2010 run of the LHC. Higher-order perturbative-QCD calculations add insight [3]. However, much can be learned about the general issues of energy, luminosity, and the relative merits of proton-proton and proton-antiproton collisionsp by comparing the luminosi- ties of parton-parton collisions as a function of s^, the c.m. energy of the colliding partons [4]. [A high-energy proton is, in essence, a broadband un- separated beam of quarks, antiquarks, and gluons.] By contemplating the parton luminosities in light of existing theoretical and experimental knowl- edge, physicists should be able to anticipate and critically examine the broad results of Monte Carlo studies. The more prior knowledge a user brings to the parton luminosities, the more useful insights they can reveal. LHC Physics Potential|2011 Run 3 Taking into account the 1=s^ behavior of the hard-scattering processes that define much of the physics motivation for a multi-TeV hadron collider, the parton luminosity Z 1 τ dLij τ=s^ (a) (b) (a) (b) ≡ dx[fi (x)fj (τ=x) + fj (x)fi (τ=x)]=x; (1) s^ dτ 1 + δij τ which has dimensions of a cross section, is a convenient measure of the reach (a) of a collider of given energy and hadron-hadron luminosity. Here fi (x) is the number distribution of partons of species i carryingp momentum fraction x of hadron a. For hadrons colliding with c.m. energy s, the scaling variable τ is given by τ =s=s: ^ (2) The cross section for the hadronic reaction a + b ! α + anything (3) is given by Z 1 X dτ τ dLij σ(s) = · · [^sσ^ (^s)] ; (4) τ s^ dτ ij!α fijg τ0 whereσ ^ij!α is the operative parton-level cross section. The (dimensionless) factor in square brackets is approximately determined by couplings. Many explicit (leading-order) forms ofσ ^ are given in Refs. [4]. The logarithmic integral typically gives a factor of order unity. If event rates for signal and backgroundsp p are known|by calculation or by measurement|for some point ( s; s^), the parton luminosities can be used to estimate the rates at other points, at an accuracy satisfactory for orien- tation. Because leading-order parton distributions have a simple intuitive interpretation, I have chosen the CTEQ6L1 leading-order parton distribu- tions [5] for the calculations presented in this note. Any of the modern sets of parton distributions will yield similar results for energy-to-energy compar- isons [6]. I present four examples relevant to discovery physics: gluon-gluon inter- actions, ud¯ interactions, interactions among generic light quarks, and inter- actions of gluons with light quarks or antiquarks. The parton luminosities 4 Chris Quigg for gluon-gluon interactions are given in Figure1. These are identical for pp andpp ¯ collisions. The parton luminosities for ud¯ interactions are plotted in Figure2. In pp collisions, ud¯ is a valence{sea combination; inpp ¯ collisions, it is valence{valence. The difference is reflected in the excess ofp the Tevatron luminosities in Figure2 over the proton-proton luminosities at s = 2 TeV. The parton luminosities for light-quark{light-quark interactions in pp colli- sions are displayed in Figure3, as examples of valence{valence interactions leading to final states such as two jets. What is plotted here is the combina- tion (u + d)(1) ⊗ (u + d)(2): (5) Forpp ¯ collisions at the Tevatron, interpret the 2-TeV curve as (u + d)(p) ⊗ (¯u + d¯)(¯p); (6) these valence{valence interactions are the main source of high-transverse- momentum jets at the Tevatron. The parton luminosities for gluon{light- quark interactions are shown in Figure4. The quantity displayed is the combination (u + d)(1) ⊗ g(2): (7) In pp collisions, the gq luminosity is twice what is shown in Figure4, cor- responding to (u + d)(1) ⊗ g(2) + g(1) ⊗ (u + d)(2). Forpp ¯ scattering at the Tevatron, interpret the 2-TeV curve as either (u + d)(p) ⊗ g(¯p) (gq collisions) or g(p) ⊗ (¯u + d¯)(¯p) (gq¯ collisions). Ratios of parton luminosities are especially useful for addressing what is gained or lost by running at one energy instead of another. Let us consider each of the example cases in turn. 2 Gluon-gluon interactions Ratios of parton luminosities for gluon-gluon interactions in p±p collisions at specified energies to the gg luminosity at the Tevatron arep shown in Fig- ure5; ratios to the LHC at design energy in Figure6. At s^ ≈ 0:4 TeV, characteristic of tt¯ pair production, Figure5 shows that the gg luminosity rises by three orders of magnitude from the 2-TeV Tevatron to the 14-TeV LHC. This rise is the source of the computed increase in the gg ! tt¯ cross LHC Physics Potential|2011 Run 5 section from Tevatron to LHC, and is the basis for the (oversimplified) slo- gan, \The Tevatron is a quark collider, the LHC is a gluon collider." Figure6 shows that the gg ! tt¯ yield drops by a bit more than a factor of 6 between ¯ 14 TeV and 7 TeV.p To first approximation, accumulating a tt sample of specified size at s = 7 TeV will requirep about 6× the integrated luminosity that would have been needed at s = 14 TeV,p although acceptance cuts should have less effect at the lower energy. At s = 10 TeV, the gg ! tt¯ prate is a factor of 2:3 smaller than at design energy.p The gg luminosity at s^ = 0:4 TeV is approximately 1:47× higher at s = 8 TeV than at 7 TeV. The dominant mechanism for light Higgs-boson production at both the Tevatron and the LHC is gg ! top-quark loop ! H, so the rates are con- trolled by the gg luminosity. For MH p≈ 120 GeV, the gg luminosity is approximately (20; 25; 38; 70)× larger at s = (7; 8; 10; 14) TeV than at the Tevatron. LHC experiments are likely to rely on the rare γγ decay of a light Higgs boson, for which high integrated luminosities will be required. At somewhat higher Higgs-boson masses, the situation could be more promising for early running. For MH = 175 GeV, a mass at which H ! ZZ becomes a significantp decay mode, the gg luminosity is roughly (30; 40; 65; 130)× larger at s = (7; 8; 10; 14) TeV than at the Tevatron. The potential Tevatron sensitivity for gg ! H ! ZZ, based on the current integrated luminos- −1 ity of 10 fb would be matchedp at the LHC by integrated luminosities of (340; 250; 160; 80) pb−1 at s = (7; 8; 10; 14) TeV. Note that these levels do not correspond to the thresholds needed for discovery (although those could be worked out, given a discovery criterion), but to the point at which the LHC would begin to break new ground, compared to the Tevatron sample now in hand. The parton-luminosity advantage of 8-TeV over 7-TeV running is 1:3 for 120-GeV gg collisions, 1:34 forp 175-GeV gg collisions, and 1:47 for 400-GeV gg collisions (see Figure7).
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